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Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources

ABSTRACT

In this paper, we consider the problem of blockwise streaming compression of a pair of correlated sources, which we term streaming Slepian-Wolf coding. We study the moderate deviations regime in which the rate pairs of a sequence of codes converges, along a straight line, to various points on the boundary of the Slepian-Wolf region at a speed slower than the inverse square root of the blocklength $n$, while the error probability decays subexponentially fast in $n$. Our main result focuses on directions of approaches to corner points of the Slepian-Wolf region. It states that for each correlated source and all corner points, there exists a non-empty subset of directions of approaches such that the moderate deviations constant (the constant of proportionality for the subexponential decay of the error probability) is enhanced (over the non-streaming case) by at least a factor of $T$, the block delay of decoding symbol pairs. We specialize our main result to the setting of lossless streaming source coding and generalize this result to the setting where we have different delay requirements for each of the two source blocks. The proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information-theoretic streaming literature. We adapt the so-called truncated memory idea from Draper and Khisti (2011) and Lee, Tan and Khisti (2015) to ensure that the effect of error accumulation is nullified in the limit of large blocklengths. We also adapt the use of the so-called minimum empirical suffix entropy decoder which was used by Draper, Chang and Sahai (2014) to derive achievable error exponents for streaming Slepian-Wolf coding.